Such a shaving apparatus is known, for example, from U.S. Pat. No. 3,710,442 issued Jan. 16, 1973. In this apparatus the cutting elements which are not in contact with the cutting plate are slightly moved outwards by the centrifugal force. This means that at the instant a cutting element during a revolution of the cutting member comes in contact with the cutting plate, rather large forces will occur to move the cutting element inwardly again in a very short period of time to a position as corresponds to the inside of the cutting plate. This will in general cause undesired vibrations in the apparatus, which moreover may lead to damage to the cutting member, the cutting plate and the other parts of the apparatus.